Many modern engineering analyses are performed with the aid of a computer system. One of such computer aided engineering (CAE) analyses is referred to as finite element analysis (FEA) or finite element method (FEM). FEA is a computer implemented method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional, non-linear structural design, and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells, and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material identifier to associate with its material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
Reinforced concrete has been used for constructing many different types of structures (e.g., buildings, dams, bridges, highways, etc.). Engineers have been relied on numerically simulated structural behaviors of reinforced concrete in FEA to make decisions improve the structural design. Prior art approaches to represent reinforced concrete structure in FEA include some ad hoc techniques, which may work properly in certain circumstances but not all incidences. It would, therefore, be desirable to have more thorough methods and systems for numerically simulating structural behaviors of reinforced concrete in finite element analysis.